On the embedding of branes in five-dimensional spaces

Details On the embedding of branes in five-dimensional spaces On the embedding of branes in five-dimensional spaces

2003-08-19

arxiv.org/abs/gr-qc/0308056v2

Class.Quant.Grav. 21 (2004) 927-934

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages - REVTEX To appear in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/21/4/012

We investigate the embedding of four-dimensional branes in five-dimensional spaces. We firstly consider the case when the embedding space is a vacuum bulk whose energy-momentum tensor consists of a Dirac delta function with support in the brane. We then consider the embedding in the context of Randall-Sundrum-type models, taking into account $Z_{2}$ symmetry and a cosmological constant. We employ the Campbell-Magaard theorem to construct the embeddings and are led to the conclusion that the content of energy-matter of the brane does not necessarily determine its curvature. Finally, as an application to illustrate our results, we construct the embedding of Minkowski spacetime filled with dust.

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